Suppose it can be made from the given tiles, then there will be 15 of them.
This is because there are 60 small squares on the board to be covered, 30
light and 30 dark.

So there must be an even number of one type of tiles and an odd number of
the other.

Now the tile type that is used an even number of times is covering an even
number of light squares and an even number of dark squares.

Also the tile type that is used an odd number of times is covering an odd
number of light squares and an odd number of dark squares (as the two
tile types both have an odd number of light and dark squares in them).

So the tiling covers an odd number of light squares and an odd number of
dark squares, which as the board actualy has an even number of both
is a contradiction. Hence no such tiling exists.